Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.80894366654422500000000.1	x^20 - 6x^19 + 22x^18 - 60x^17 + 138x^16 - 279x^15 + 510x^14 - 852x^13 + 1314x^12 - 1878x^11 + 2469x^10 - 2934x^9 + 3108x^8 - 2916x^7 + 2406x^6 - 1710x^5 + 1008x^4 - 468x^3 + 160x^2 - 36x + 4	\( 2^{8}\cdot 3^{18}\cdot 5^{10}\cdot 17^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial
20.0.114840714180513475067904.1	x^20 - 4x^19 + 13x^18 - 30x^17 + 66x^16 - 130x^15 + 243x^14 - 404x^13 + 622x^12 - 866x^11 + 1112x^10 - 1264x^9 + 1267x^8 - 1094x^7 + 842x^6 - 554x^5 + 309x^4 - 138x^3 + 56x^2 - 12x + 1	\( 2^{20}\cdot 3^{14}\cdot 389^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial
20.4.140124985753600000000000000.1	x^20 - 4x^19 + 14x^18 - 24x^17 + 35x^16 - 4x^15 - 52x^14 + 140x^13 - 139x^12 + 28x^11 + 108x^10 - 128x^9 + 55x^8 + 16x^7 + 110x^6 + 32x^5 + 25x^4 + 24x^3 + 36x^2 + 12x - 1	\( 2^{38}\cdot 5^{14}\cdot 17^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial
20.4.1031221647769600000000000000.1	x^20 - 4x^19 + 10x^18 - 24x^17 + 20x^16 + 4x^15 - 84x^14 + 132x^13 - 203x^12 + 100x^11 - 82x^10 - 148x^9 + 204x^8 - 424x^7 + 528x^6 - 532x^5 + 449x^4 - 392x^3 + 298x^2 - 96x + 4	\( 2^{46}\cdot 5^{14}\cdot 7^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial (GRH)
20.12.6146560000000000000000000000.1	x^20 - 10x^18 + 15x^16 + 120x^14 - 435x^12 + 60x^10 + 1875x^8 - 3550x^6 + 2725x^4 - 900x^2 + 100	\( 2^{30}\cdot 5^{22}\cdot 7^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial (GRH)
20.12.26623100852415561676025390625.1	x^20 - 15x^18 + 80x^16 - 20x^15 - 225x^14 + 255x^13 + 575x^12 - 1405x^11 - 1299x^10 + 3810x^9 + 865x^8 - 4310x^7 + 1155x^6 + 990x^5 - 475x^4 - 120x^3 + 75x^2 + 15x - 1	\( 3^{4}\cdot 5^{22}\cdot 13^{10} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial (GRH)
20.20.13275219335584153600000000000000.1	x^20 - 8x^19 - 2x^18 + 156x^17 - 258x^16 - 858x^15 + 2080x^14 + 1992x^13 - 6342x^12 - 2464x^11 + 9113x^10 + 2464x^9 - 6342x^8 - 1992x^7 + 2080x^6 + 858x^5 - 258x^4 - 156x^3 - 2x^2 + 8x + 1	\( 2^{30}\cdot 5^{14}\cdot 1193^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial (GRH)
20.20.54736322560000000000000000000000.1	x^20 - 40x^18 - 20x^17 + 565x^16 + 404x^15 - 3750x^14 - 3220x^13 + 12360x^12 + 12680x^11 - 18848x^10 - 24300x^9 + 9470x^8 + 19500x^7 + 1010x^6 - 6404x^5 - 1805x^4 + 600x^3 + 320x^2 + 40x + 1	\( 2^{38}\cdot 5^{22}\cdot 17^{4} \)	$D_5\wr C_2:C_2$ (as 20T96)	Trivial (GRH)